The first salvo came from Hamilton, Bermuda-based Aspen, which announced that its board of directors had unanimously agreed on Tuesday to reject an updated offer that Endurance made to acquire all of the outstanding shares of Aspen for a combination of common stock and cash valued at $3.2 billion.

“The Aspen board of directors is unanimous in its belief that the Endurance offer significantly undervalues Aspen and fails to reflect the value of our business and strong future prospects,” Aspen Chairman Glyn Jones said in a statement.

The Aspen statement listed eight reasons why the board was against the deal including questions about the value of Endurance stock, the nature of the $ 1.0 million bridge loan that Endurance would use to finance the deal and Endurance's business mix, especially its crop insurance business.

“Endurance has historically underperformed, and there are a number of reasons why Aspen does not believe Endurance's claims about its prospects and believes that Endurance's stock is not an attractive currency, particularly in comparison to Aspen's shares,” the statement reads.

Furthermore, Aspen said it has filed a preliminary revocation solicitation statement with the U.S. Securities and Exchange Commission to stop Pembroke, Bermuda-based Endurance's plan to force a meeting of Aspen shareholders under Bermuda law at which shareholders would vote on a proposal to increase the size of Aspen's board.

Mr. Jones said Endurance's invocation of Bermuda shareholders' law amounted to “desperate attempts to force through an inadequate offer” for Aspen.

“We strongly urge shareholders not to support Endurance's pursuit of an involuntary scheme of arrangement,” he said. “If it proceeds, this convoluted legal maneuver could result in a 'take-it or leave-it' shareholder vote on a transaction under the terms currently proposed by Endurance.”

The riposte from Endurance was swift, criticizing the “combative response” from Aspen.

Endurance Chairman and CEO John R. Charman said Endurance's legal actions were intended to “give Aspen shareholders a voice” and to urge Aspen to come to the negotiating table.

“We know from our extensive engagement with Aspen shareholders that many have been frustrated by the dismissive and entrenched response of Aspen's board and management to the significant opportunity for value creation that Endurance has proposed,” Mr. Charman said in a statement.

The statement also offered a point-by-point rebuttal of Aspen's enumerated reasons for rejecting the deal. For example, Endurance said its use of a $1.0 billion bridge loan for the cash component of the transaction was not unusual.

Elsewhere, the company defended its operational record and financial performance, stating that Endurance's combined ratio averaged 95.6% over the past five years, compared with 96.7% for Aspen. “Endurance finds Aspen's statements regarding the value of Endurance's shares particularly misleading given Endurance's consistent outperformance of Aspen over the past five years,” the statement reads.

Mr. Charman said the company would use a two-pronged attack to see the deal through: convening a special general meeting to increase the size of the Aspen board, which will lead to a majority of Aspen's directors standing for election at its 2015 annual general meeting, and endorsing the pursuit of a “court-sanctioned” scheme of arrangement.

“We are truly committed to pursuing these and any other actions and are determined to see them through in order to provide Aspen shareholders the ability to realize the highly attractive premium our proposal represents,” Mr. Charman said.

Endurance launched a hostile takeover bid against Aspen in April after a “friendly dialogue” between the two companies in January 2014 failed to produce a deal.